Persson, Johan

Abstract [en]

In this thesis work numerical procedures are developed for modeling dynamic fracture of discontinuous materials, primarily materials composed of a load-bearing network. The models are based on the Newtonian equations of motion, and does not require neither stiffness matrices nor remeshing as cracks form and grow. They are applied to a variety of cases and some general conclusions are drawn. The work also includes an experimental study of dynamic crack growth in solid foam. The aims are to deepen the understanding of dynamic fracture by answering some relevant questions, e.g. What are the major sources of dissipation of potential energy in dynamic fracture? What are the major differences between the dynamic fracture in discontinuous network materials as compared to continuous materials? Is there any situation when it would be possible to utilize a homogenization scheme to model network materials as continuous? The numerical models are compared with experimental results to validate their ability to capture the relevant behavior, with good results. The only two plausible dissipation mechanisms are energy spent creating new surfaces, and stress waves, where the first dominates the behavior of slow cracks and the later dominates fast cracks. In the numerical experiments highly connected random fiber networks, i.e. structures with short distance between connections, behaves phenomenologically like a continuous material whilst with fewer connections the behavior deviates from it. This leads to the conclusion that random fiber networks with a high connectivity may be treated as a continuum, with appropriately scaled material parameters. Another type of network structures is the ordered networks, such as honeycombs and semi-ordered such as foams which can be viewed as e.g. perturbed honeycomb grids. The numerical results indicate that the fracture behavior is different for regular honeycombs versus perturbed honeycombs, and the behavior of the perturbed honeycomb corresponds well with experimental results of PVC foam.

Abstract [en]

A new discrete element model to deal with rapid deformation and fracture of flat fibrous materials is derived. The method is based on classical mechanical theories and is a combination of traditional particle dynamics and nonlinear engineering beam theory. It is assumed that a fiber can be seen as a beam that is represented by discrete particles, which are moving according to Newton's laws of motion. Damage is dealt with by fracture of fiber-segments and fiberfiber bonds when the potential energy of a segment or bond exceeds the critical fracture energy. This allows fractures to evolve as a result of material properties only. To validate the model, four examples are shown and compared with analytical results found in literature. Copyright (c) 2013 John Wiley & Sons, Ltd.

Abstract [en]

A mechanical model for analyses of rapid deformation and fracture in three-dimensional fiber materials is derived. Large deformations and fractures are handled in a computationally efficient and robust way. The model is truly dynamic and computational time and memory demand scales linearly to the number of structural components, which make the model well suited for parallel computing. The specific advantages, compared to traditional continuous grid-based methods, are summarized as: (1) Nucleated cracks have no idealized continuous surfaces. (2) Specific macroscopic crack growth or path criteria are not needed. (3) The model explicitly considers failure processes at fiber scale and the influence on structural integrity is seamlessly considered. (4) No time consuming adaptive re-meshing is needed. The model is applied to simulate and analyze crack growth in random fiber networks with varying density of fibers. The results obtained in fracture zone analyses show that for sufficiently sparse networks, it is not possible to make predictions based on continuous material assumptions on a macroscopic scale. The limit lies near the connectivity l(c)/L = 0.1, where is the ratio between the average fiber segment length and the total fiber length. At ratios l(c)/L < 0.1 the network become denser and at the limit l(c)/L -> 0, a continuous continuum is approached on the macroscopic level. (C) 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license.

Abstract [en]

Dynamic fracture behavior in both fairly continuous materials and discontinuous cellular materials is analyzed using a hybrid particle model. It is illustrated that the model remarkably well captures the fracture behavior observed in experiments on fast growing cracks reported elsewhere. The material's microstructure is described through the configuration and connectivity of the particles and the model's sensitivity to a perturbation of the particle configuration is judged. In models describing a fairly homogeneous continuous material, the microstructure is represented by particles ordered in rectangular grids, while for models describing a discontinuous cellular material, the microstructure is represented by particles ordered in honeycomb grids having open cells. It is demonstrated that small random perturbations of the grid representing the microstructure results in scatter in the crack growth velocity. In materials with a continuous microstructure, the scatter in the global crack growth velocity is observable, but limited, and may explain the small scattering phenomenon observed in experiments on high-speed cracks in e.g. metals. A random perturbation of the initially ordered rectangular grid does however not change the average macroscopic crack growth velocity estimated from a set of models having different grid perturbations and imply that the microstructural discretization is of limited importance when predicting the global crack behavior in fairly continuous materials. On the other hand, it is shown that a similar perturbation of honeycomb grids, representing a material with a discontinuous cellular microstructure, result in a considerably larger scatter effect and there is also a clear shift towards higher crack growth velocities as the perturbation of the initially ordered grid become larger. Thus, capturing the discontinuous microstructure well is important when analyzing growing cracks in cellular or porous materials such as solid foams or wood.